On packing designs with block size 5 and indices 3 and 5

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Abstract

Let V be a finite set of order υ. A (υ,κ,λ) packing design of index λ and block size κ is a collection of κ-element subsets, called blocks, such that every 2-subset of V occurs in at most λ blocks. The packing problem is to determine the maximum number of blocks, σ(υ,κ,λ), in a packing design. It is well known that σ(υ,κ,λ) ≤ [υ/κ[υ-1/κ-1 λ]] = ψ(υ,κ,λ), where [x] is the largest integer satisfying x ≥ [x]. It is shown here that σ(υ,5,3) = ψ(υ,5,3) for all υ ≡ 3 (mod 4) and σ(υ,5,5) = ψ(υ,5,5) for all positive integers υ ≥ 5 with the possible exceptions of υ = 28, 32, 34.

Original languageEnglish
Pages (from-to)23-48
Number of pages26
JournalAustralasian Journal of Combinatorics
Volume13
StatePublished - 1996

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